Ideas of Henri Poincaré, by Theme

[French, 1854 - 1912, Professor of Mathematics at the Sorbonne.]

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6. Mathematics / A. Nature of Mathematics / 2. Geometry

10245

One geometry cannot be more true than another

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite

15923

Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Lavine]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

10180

Mathematicians do not study objects, but relations between objects

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism

9916	Convention, yes! Arbitrary, no! [Putnam]

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism

18203

Avoid non-predicative classifications and definitions

26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature

15877

The aim of science is just to create a comprehensive, elegant language to describe brute facts [Harré]